Diaschismic family: Difference between revisions

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Those all keep the same half-octave period and fifth generator.

* Bidia adds [[3136/3125]], the hemimean comma.

Bidia adds [[3136/3125]], the hemimean comma, with a 1/4-octave period. Shrutar adds [[245/243]] and shru adds [[392/375]], with a quartertone generator. Sruti adds [[19683/19600]] and anguirus adds [[49/48]], with a neutral third or hemitwelfth generator. Those split the original generator in two. Echidna adds [[1728/1715]], the orwellisma, with a ~9/7 generator. Echidnic adds [[686/675]], the senga, with a ~8/7 generator. Those split the original generator in three. Finally, quadrasruta adds [[2401/2400]] and splits the original generator in four.

* Echidna adds [[~~1728~~/~~1715~~]], the ~~orwellisma~~.

* Shrutar adds [[~~245~~/~~243~~]], the ~~sensamagic comma.~~

~~Shrutar has~~ a generator ~~of a quartertone (which can be taken as~~ [[36/35]], the ~~septimal quartertone) and echidna has~~ a ~~generator of 9~~/7. ~~Bidia has a quarter-octave period~~ and ~~a fifth~~ generator.

==== Subgroup extensions ====

Since the diaschisma factors into ([[256/255]])<sup>2</sup>([[289/288]]) in the 17-limit, it extends naturally to the 2.3.5.17 subgroup as ''srutal archagall'', documented right below. The [[S-expression]]-based comma list of this temperament is {[[256/255|S16]], [[289/288|S17]]}.

=== Srutal archagall ===

@@ Line 41: / Line 41: @@
 Those all keep the same half-octave period and fifth generator.
-* Bidia adds [[3136/3125]], the hemimean comma.
+Bidia adds [[3136/3125]], the hemimean comma, with a 1/4-octave period. Shrutar adds [[245/243]] and shru adds [[392/375]], with a quartertone generator. Sruti adds [[19683/19600]] and anguirus adds [[49/48]], with a neutral third or hemitwelfth generator. Those split the original generator in two. Echidna adds [[1728/1715]], the orwellisma, with a ~9/7 generator. Echidnic adds [[686/675]], the senga, with a ~8/7 generator. Those split the original generator in three. Finally, quadrasruta adds [[2401/2400]] and splits the original  generator in four.
-* Echidna adds [[1728/1715]], the orwellisma.
-* Shrutar adds [[245/243]], the sensamagic comma.
-Shrutar has a generator of a quartertone (which can be taken as [[36/35]], the septimal quartertone) and echidna has a generator of 9/7. Bidia has a quarter-octave period and a fifth generator.
 ==== Subgroup extensions ====
 Since the diaschisma factors into ([[256/255]])<sup>2</sup>([[289/288]]) in the 17-limit, it extends naturally to the 2.3.5.17 subgroup as ''srutal archagall'', documented right below. The [[S-expression]]-based comma list of this temperament is {[[256/255|S16]], [[289/288|S17]]}.
 === Srutal archagall ===